RECENT ADVANCES IN SCIENCE 281 



work of Cowell, Rutherford, Stoney, Joly, Sollas and others, 

 on the subject is also criticised. 



In the application of mathematical methods to physical 

 phenomena, it is obviously very important that one should be 

 able sometimes to follow out what goes on, by geometrical con- 

 ceptions, without blind calculation. Sometimes such calcu- 

 lations are necessary and advantageous from the point of view 

 of generality and economy of effort, as we see in Lagrange's 

 Mecanique. But vector methods, for example, give us far 

 greater insight, and insight is often prized, perhaps rightly, 

 even above generality. In the theory of the gyroscope, ^Prof. 

 Horace Lamb (Proc. Roy. Soc. Edinb. 191 5, 35) obtains the 

 intrinsic equations and shows that, besides their uses as a basis 

 of calculation, they enable us to foresee the general character 

 of the motion in cases where the actual calculation would be 

 difficult. 



The analogy between paths of particles and forms of strings, 

 on the one hand, and the paths of rays of light on the other, 

 is familiar to all who have studied the applications of the 

 principle of least action ; and Prof. Levi Civita (Atti dei Lincei, 

 191 5, 24), gives a general dynamical investigation of certain 

 reciprocal theorems in optics due to Helmholtz and Straubel, 

 which is based on this analogy. 



ASTRONOMY. By H. Spencer Jones, M.A., B.Sc, Royal Observatory, 

 Greenwich. 



The Age of the Earth. — It has been generally assumed that the 

 conclusion reached by Lord Kelvin from his discussion of the 

 age of the Earth — viz. that the temperature of the Earth's 

 crust cannot have been near its present value for much more 

 than twenty or thirty million years — has been invalidated by 

 the discovery of radioactive elements, and that in this way 

 the much greater latitude required by the theory of tidal friction 

 and by geologists might be accounted for. In a letter to 

 Nature (vol. 95, p. 204, 191 5, April 22) Dr. F. A. Lindemann 

 argues against such a conclusion. Lord Kelvin's estimate 

 was based upon three independent considerations — the tem- 

 perature gradient inside the Earth's crust, the amount of 

 tidal friction, and the total amount of energy radiated by the 

 Sun. The first of these arguments has been invalidated by 

 the discovery of radioactivity. Since, however, the tempera- 



